DearMHFResidents,

I need the proof of theLaplace inversion formula

$\displaystyle f(t)=\displaystyle\frac{1}{2\pi\mathrm{i}}\display style\int_{\sigma-\mathrm{i}\infty}^{\sigma+\mathrm{i}\infty}F(z)\ma thrm{e}^{tz}\mathrm{d}z,$

where $\displaystyle \sigma$ is a sufficiently large real number, without using theFourier transform.

Can you please help me in this direction?

bkarpuz